82 E.W. Blake on the flow of Elastic Fluids through Orifices. 
Thus we have found for the value of D, D= 3 a dis nae 
greater than — if otherwise, D=d. And for the value of P 
(since P= A — D) we have p=9 if d is not greater than S, 
if otherwise, P= A —d. 
DSVP 
In applying the general dynamic law VDS x VD to the 
ease of elastic fluids, the values * D and P should therefore be 
assigned in accordance with this 
e have already remarked te. treatises on the dynamics of 
fluids, in applying the above general expression to elastic fluids, 
put D as equal to A, and P asequal to A —d inall cases. This, 
as will appear from the above rule, makes D too large in all cases ; 
and P also too large whenever d is less than half A. In the case 
of a discharge into a vacuum, it makes each of these quantities 
double what it should be. In Sess a formula to express 
the velocity of the flow into a vacuum, err an 
other ; so that in that particular case the be is the same as if 
the values of these quantities were assigned in accordance “— 
¢ » 
our rule; for by our rule Yorn ad and by the old le 
JF 
A 
Again, since J5 a is a constant quantity however A may a : 
aa 
it follows from our he that the velocity of the flow into a vacuut 
isa constant quantity, being the same for every density in the 
discharging vessel. The same also results from the old eon 
flow into a vacuum in a given time, the results of the two rules 
will differ widely. For, since the old rule gives the velocity of 
the flow correctly, and at the same time puts its density at double 
what it should be, it follows that the old rule makes the quantisy 
discharged i in a given time double what it should be. is 
Hence it appears that in a steam engine, the valves and pipes 
which convey the steam from the working cylinder to the con- 
denser, must be of double the size that would be assigned to them 
oy th in order to discharge the contents of the working cyl- 
inder in a ‘ghia time, without increased reaction neem the: piston. 
